The canonical model of a singular curve

We give refined statements and modern proofs of Rosenlicht’s results about the canonical model C ′ of an arbitrary complete integral curve C . Notably, we prove that C and C ′ are birationally equivalent if and only if C is nonhyperelliptic, and that, if C is nonhyperelliptic, then C ′ is equal to the blowup of C with respect to the canonical sheaf ω . We also prove some new results: we determine just when C ′ is rational normal, arithmetically normal, projectively normal, and linearly normal.